def generate_polytope_data(coxeter_diagram,
trunc_type,
extra_relations=(),
snub=False,
dual=False):
"""
Generate polyhedra vertex coordinates and face indices.
The result is output to the file `data.frag`.
"""
if snub:
P = models.Snub(coxeter_diagram, extra_relations=extra_relations)
else:
P = models.Polyhedra(coxeter_diagram, trunc_type, extra_relations)
if dual:
P = models.Catalan3D(P)
P.build_geometry()
vertices_coords = P.vertices_coords
def get_oriented_faces(face_group, name):
"""The faces returned by `P.build_geometry()` may not have their
normal vectors pointing outward, we need to rearange them in the
right order before sending them to the gpu.
"""
m = len(face_group)
n = len(face_group[0])
faces_data = np.zeros((m, n, 3), dtype=float)
for ind, face in enumerate(face_group):
face_coords = [vertices_coords[ind] for ind in face]
face_center = sum(face_coords) / len(face)
v0, v1, v2 = face_coords[:3]
normal = np.cross(v1 - v0, v2 - v0)
if np.dot(face_center, normal) < 0:
face_coords = face_coords[::-1]
faces_data[ind, :, :] = face_coords
faces_data = faces_data.reshape(m * n, 3)
vec_string = ",\n".join(f" vec3({x}, {y}, {z})"
for x, y, z in faces_data)
return (f"#define {name}Enabled {n}\n\n" +
f"vec3[{m * n}] {name} = vec3[{m * n}](\n{vec_string}\n);\n\n")
result = get_oriented_faces(P.face_indices[0], "facesA")
if len(P.face_indices) > 1:
result += get_oriented_faces(P.face_indices[1], "facesB")
if len(P.face_indices) > 2:
result += get_oriented_faces(P.face_indices[2], "facesC")
with open(os.path.join(GLSL_DIR, "data.frag"), "w") as f:
f.write(result)
def anim(
coxeter_diagram,
trunc_type,
extra_relations=(),
snub=False,
description="polytope-animation",
):
"""
Call POV-Ray to render the frames and call FFmpeg to generate the movie.
"""
if len(coxeter_diagram) == 3:
if snub:
P = models.Snub(coxeter_diagram, extra_relations=extra_relations)
else:
P = models.Polyhedra(coxeter_diagram, trunc_type, extra_relations)
scene_file = "polyhedra_animation.pov"
elif len(coxeter_diagram) == 6:
P = models.Polychora(coxeter_diagram, trunc_type, extra_relations)
scene_file = "polytope_animation.pov"
elif len(coxeter_diagram) == 10:
P = models.Polytope5D(coxeter_diagram, trunc_type, extra_relations)
scene_file = "polytope_animation.pov"
else:
raise ValueError("Invalid Coxeter diagram: {}".format(coxeter_diagram))
P.build_geometry()
# POV-Ray does not support 5d vectors well, so project the vertices in python
if isinstance(P, models.Polytope5D):
P.proj4d()
vert_data, edge_data, face_data = P.get_povray_data()
with open(data_file, "w") as f:
f.write(POV_TEMPLATE.format(vert_data, edge_data, face_data))
subprocess.call(POV_COMMAND.format(scene_file, description), shell=True)
subprocess.call(FFMPEG_COMMAND.format(description, description),
shell=True)
return P